Question

Problem 3 (200 pts): For a driven shaft of a gearbox, one possible shaft layout is shown in the top figure. Both bearings and the gear will be located against shoulders. The gear and the motor will transmit the torque through the keys. The bearings can be lightly pressed onto the shaft. The left bearing will locate the shaft in the housing, while the right bearing will float in the housing. Shear force, bending moment, and torque diagrams are shown in the bottom figure. (a) Determine potential critical locations for stress design. (b) Determine critical diameters of the shaft based on fatigue and static stresses at the critical locations. (e) Make any other dimensional decisions necessary to specify all diameters and axial dimensions. Sketch the shaft to scale, showing all proposed dimensions. (d) Determine the minimum fatigue factor of safety by evaluating at any critical locations. Use the DE-Goodman fatigue criterion for 1030HR.

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Answer 1

ARISHER. Anestleri A driven shaft of a gearbox, one possible Shaft & the gear will be located againt Shoulders. The gear & the motor will tranmit . the forque through the keys. The left bearing will tocate the shaft on the housing, white the right bearing will float on the housing. Shear force, bending moment, & toque dioglana at Delo 0.15 a) The critical locations for strean design. Stear force, Bending moment & Torque en maxmom at the location naq an from a. artere moment is maximon that occora maximum bending stream

k qin aink 6an Bending stream (f) = M y food Di78 Td 22185 psi d3 li, allhere the Torque ex manimom (n=9 in) iej (1= 2500 lbf in) that occur maximum shear strean. . Shear strear at nog in 2500 d . idy x 32 12732.4 - psi d3 ... Critical location in dag in from A. (for Stream designs.

b) Critical diameters of the shaft bared on fatique & Static stremen at the critical location. For 1030 HR, Pensile strength = 76100 psi Coltimate) Yield tensile stren . 63800 psi. Por critical diameter factor of safety = 1. According to marmom principal strean thady. 050)+167)7x 79,51) )+(37)+z2.com FOS 18 22185 12 800. (*)•)(*) Bern) : 6.0 (1995) • Jeans you can us] = 6.- 18 1127 32 4 12 63,900 2 97979.109 = 63,800. d3 - do 0.759 Pn.

d~ 6.16 inch. .: Critical diameter of shaft (d) = 0.76 inch. 242 tbf-in - 1088 abf.

(6) Size factor Joog bencing & Dorsion 0.11 ki se o istom T. 62 = 0.7759 Sengele Pactor Ks = 4.51 (2) 0.26 -0.26 = 4.51 x (7.6100) ks = 0.24.26 Falīgue schenke gaster → mar No need any other dimensional necessary to Specigg diameters. (d) from maximum principal stress theory (dz 0.76%) minimum principal stress,

B = (2) { 2 ) + 23195,- 82185 > 3732.4 V 39185 - 2xo.163 ) 1978 A 280.7637 0.763 imum rz = -13,199.147 psi maximum principal stress, 'Di = 63800 psi m = 7+3 63800 - C13199.147) iv 2 m = 25, 300 psi = -D 63800 - (13199.147) .: Ta .: Ta = - - - Pa = 38,500 psi. men Lube from the Goodman Line 38500 25300 + - 76100 76100 [fos = 12

Goodman Line (stres pailere) K im I L a rut (m) from DE - Goodman, minimum Doctor of Safety (por any critical Location = 12